Glossary — M09: Option Replication Using Put-Call Parity

Term	Definition
Protective put	A portfolio of long stock + long put; provides downside protection while maintaining upside participation. Payoff: $max (S_{T}, X)$
Fiduciary call	A portfolio of long call + risk-free bond (face value $X$ ); produces the same payoff as a protective put: $max (S_{T}, X)$
Put-call parity	The no-arbitrage relationship linking European call and put prices: $S_{0} + p_{0} = c_{0} + X / (1 + r)^{T}$
Synthetic call	A position replicating a call option: long stock + long put + borrow PV of strike
Synthetic put	A position replicating a put option: long call + short stock + lend PV of strike
Synthetic stock	A position replicating long stock: long call + short put + lend PV of strike
Synthetic bond	A position replicating a risk-free bond: long stock + long put + short call (covered call + protective put)
Put-call forward parity	Put-call parity using the forward price: $F_{0} (T) / (1 + r)^{T} + p_{0} = c_{0} + X / (1 + r)^{T}$
Covered call	A portfolio of long stock + short call; generates premium income but caps upside at the strike price
Conversion	An arbitrage strategy exploiting put-call parity violations: long stock + long put + short call = synthetic bond; compare yield to actual risk-free rate

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